Acoustic horn



Jan. 4, 1944. v. SALMQN 2,338,262

ACOUSTIC HORN Filed July 23, 1942 3 Sheets-Sheet 1 --oxis Jan. 4, 1944. v SALMON 2,338,262

ACOUSTIC HORN Filed July 23, 1942 3 Sheets-Sheet 2 3 9 o 15 2 T a T=.7o7 .a'

Ratio of Throat Resistance to Ultim n l 'v'2"2 3 4v56789IO Ratio of Frequency to Cut-Off Frequency fiviz/af '20 Zzkzaezz/Ja/zzzazz fiy= (TM MM V.SALMON ACOUSTIC HORN Jan. 4, 1944.

Filed July 23, 1942 3 Sheets-Sheet I5 l a n e n n o w l. w x E I.\ 15%... 6 O 2 if. 0 J O T [I in I 0 5 O 5 O 5 O 2 2 l l 250 3a EE w Frequency five/22%;? $255622? Ja/mazz fly Inn L awQ Patented Jan. 4, 1944 ACOUSTIC HORN Vincent Salmon, Chicago, 111., assignor to Jensen Radio Manufacturing Company, Chicago, 111., a corporation oi. Nevada Application July 23, 1942, Serial No. 452,112

17 Claims.

This invention relates to acoustic devices and in particular to acoustic horns of the type used with sound radiators or receivers, or used as a means for coupling acoustic conduits of diflerent sizes or having different terminal impedances.

The ultimate objective of this invention is a sound reproducer or radiator, such as a radio loudspeaker, or a sound receiving device, such as a radio microphone, having high electroacoustic conversion efficiency which is uniform over a wide range of frequencies, the novel contribution toward the achievement of this objective being a horn, or, rather, a family of home whose acoustic impedance characteristics are adjustable over a wide range. The great flexibility of this family of horns permits a closer approach to the attainment of optimum terminal impedance conditions under a wider variety of circumstances than has heretofore been possible.

The invention is more specifically directed to the improvement of the emciencies of the acoustic devices mentioned above in the lower frequency ranges.

Subsidiary objects of the invention include the provision of a horn whose throat resistance rises at a predetermined rate with increasing frequencies immediately above the cut-ofi frequency and whose throat reactance characteristics can be adjusted within wide practical limits to annul over a part of the low frequency range the negative reactance of the associated mechanical or acoustical driving devices, including their associated electrical signal sources, in order that high power factor conditions may obtain.

An outstanding and most useful feature of the invention resides in the ability of a properly se- 6 The horn is illustrated and certain of its characteristics are indicated in ing drawings, in which Fig. 1-15 a sideelevational view of a sound the accompany:

radiator or receiver,-the horn being shown in u longitudinal section and following the contours defined by the within equation where T=0.6;

Fig. 6 contains profiles of horns, for comparison purposes, for three values of the parameter of the horn equation given herein;

Fig. 3 is a chart indicating resistance characteristics of the horn for five values of the parameter;

Fig. 4 is a chart showing the experimentally determined relative efficiency-frequency characteristics of an exponential horn and of the horn of the invention where the equation parameter, T, is 0.6, both horns having the same cut-off frequencies and mouth areas;

Fig. 5 is a diagrammatic view in longitudinal section of a horn of the re-entrant type embodying the invention.

The contribution of the horn to the radiating efliciency of a, horn loudspeaker depends, not merely upon the structure of the horn considered as a separate element, but also upon the relationship of the mechanical impedance looking toward the diaphragm of the driving motor with its associated electrical signal source, referred'to herein as the driver impedance, to the mechanical impedance at the throat of the horn looking toward its mouth, this latter value being referred to herein as the horn throat impedance. The ideal arrangement from the standpoint of radiating efficiency of the loudspeaker would be one in which the acoustic loading of the driver diaphragm furnished by the horn is such that the driver impedance and the horn throat impedance are conjugate; that is, the resistances are equal while the reactances are equal in magnitude and opposite in sign. This condition can be readily obtained with simple acoustical elements at a single frequency but can only be approached in actual practice over a range of frequencies for the reason that both the driver impedance and that of the horn throat vary independently over the useful frequency range. Since the greatest changes, especially in horn characteristics, occur in the lower frequency ranges, it is in this region that horn design exerts greatest influence on the overall response of the speaker unit.

Considering, first, the nature of the driver impedance which must be matched by the horn, it

0 may be stated that the resistance component of this impedance is approximately constantover the low frequency range. It follows that for high and uniform overall efllciency the horn throat resistance should be as nearly constant as possible and equal to the resistance component of the driver impedance. of the several types of horns heretofore known to the art, the exponential type most nearly approaches this requirement. As will be shown hereinafter, the present invention encompasses horns which meet this requirement to a substantially greater extent.

While resistance considerations are generally determinative of the particular horn structure to be used with a given driving motor, the reactance -component of the driver and horn throat impedances is generally a factor to be considered and may, in certain circumstances, be controlling. Where the cut-off frequency of the horn (the frequency below which the acoustic resistance of the horn is zero) is below the resonant frequency of the driving motor with the impedance on the horn side of the diaphragm reduced to zero, it is possible to substantially match and annul the reactance of the driver, which, in this range, is capacitative, by means of a. properly selected member of the horn family herein described. The throat reactance of such a horn will be positive and its average value will decrease with increasing frequency. With the correct resistance characteristic this reactance annulling results in a system which approaches a conjugate match of impedances with consequently improved efiiciency of power transfer to the atmosphere.

Fig. 1 of the drawings illustrates an acoustic device which may be taken to be either a loudspeaker comprising a horn Iii, shown in section, and driving motor I I, or a sound receiving device in which case the element I I would be a pressure sensitive ac'ousto-electric transducer. In this simple form of horn the axis, which is represented by the broken line bearing the legend axis, is a straight line. Considering the device here illustrated as a loudspeaker, sound generated by the vibrating diaphragm of the driving motor II enters the horn at the throat l2, traveling through the horn and emerging into the atmosphere at the mouth l3 of the horn. The impedance characteristics of the acoustic load furnished to the diaphragm by the horn depends upon the interior configuration of the horn, or more specifically, the manner in which the crosssectional area of the horn increases with distance from the throat. Whether the horn is of the simple, straight type, as illustrated in Fig. 1, or of the coiled, folded, or re-entrant type, or whether the cross-section is circular, rectangular, or of some other configuration, the axis of the horn is defined as the locus of points marking the mean or average of the acoustic path or channel provided by the horn. In the case of an annular passage, the mean path is a surface rather than a line. The cross-sectional area. at any point within the horn is the area of a surface which is perpendicular to its axis or mean acoustic path and bounded by the walls of the horn. For example, the cross-sectional area of the horn at a distance, x, from the throat I2 is the area, S, of the plane indicated by the line so designated in Fig. 1. The smallest area of the horn is that of the throat, St, and the largest area is that of the mouth.

In accordance with the invention, the crosssectional area of horn l0 increases from a. value, St, at the throat in accordance with the following definition:

assaeee In this equation,

S=cross-sectional area at distance a: from the throat of the horn measured along mean acoustic path thereof,

cosh

is the hyperbolic cosine function of the argument sinh o is the hyperbolic sine function of the argument 0 being the velocity of a plane sound wave in unbounded atmosphere and in the cut-off frequency of the horn,

and T is a constant, a parameter which determines the character of the flare of a given horn. The family of horns embraced by this invention falls within the outer limits established by values of T equal to zero and infinity. A self-consistent set of units must, of course, be used in calculations, involving the equation. As used herein, the expressions, "positive finite value" and "positive value shall be taken to include zero.

Although the claims specifically define the scope of the invention, in order to avoid any misconception it is pointed out here that when the parameter, T, is assigned a value of unity, the horn equation given above reduces to a function which defines the well known exponential horn, and when the value of T is infinite, the relationship reduces to a function which defines a conical horn which is also known in the art. These special members of the family are expressly disclaimed from the scope of the invention herein claimed.

The horn defined by the above equation when T is assigned a value of zero is the special case which results in a slope of zero at its throat with respect to its axis. In this case the horn equation reduces to the form When designing a. horn for a particular application, many factors must be taken into consideration. The art is well aware of the bearing of such considerations as throat and mouth sizes and shapes, the materials of which the horn is constructed and the thickness of the walls. In proceeding with the specification of a horn in accordance with the present invention, it is first necessary to arrive at a tentative determination of the value of the parameter T. This selection depends upon the characteristics which the complete loudspeaker is to possess and upon the impedance characteristics of the 'driving motor. Knowing these, the response of different members of the horn family (that is, for different values to T) may be predetermined. The curves of Fig. 3 show the relationship between acoustic resistance at the throat of the horn and the frequency of the sound input. They show that an ultimate value is approached by all members of the horn family in the higher frequency range. For the reasons stated above. these curves may also be used to predict the relative acoustic output or the several horns of the family. Accordingly, if high efllciency immediately above cut-off is desired with uniformity over the broadest possible range, a value of T less than 1, say 0.6, is selected. If constancy of response over a wide range of frequencies is the desired objective, a value of T greater than 1 is to be chosen.

Having selected a value for T, the cut-off frequency )o is chosen. This will be near the lowest frequency to be reproduced by the loudspeaker and its exact value will depend upon engineering and economic factors. Then the throat area, St,

may be determined from a consideration of the impedance characteristics of the driving motor. This is a process which, while somewhat complicated, is well understood by those skilled in the art. In a particular example, when the horn is to be used in association with a driving unit having a diaphragm area of four square inches and an unloaded resonant frequency of about 200 cycles per second, the value of Sn would be approximately 1.? square inches.

With values assigned to T, in, and St, the crosssectional area of the horn at any point, IL, may be determined from the law given above. The length of the horn, or, to put the limitation in terms of the controlling dimension, the area of the horn mouth depends upon the fidelity of reproduction to be achieved. The larger the area of the horn mouth, the better it radiates low frequency sounds. The ideal horn is. of infinite 1ength and mouth area. However, it is generally recognized that reflections of the sound wave emerging at the horn mouth are negligible, when motor, where, in the case of the circular horn, the

mouth area is such that its circumference is greater than the wave length of the sound of lowest frequency to be transmitted. Where the horn mouth is, or approximates, the shape of a regular polygon, this limitation may be stated in terms of an equivalent circular horn mouth, that is, the mouth of a hypothetical circular horn having the same area. With certain adjustments in the driving system, this limiting horn mouth circumference may be reduced by 50% without causing objectionable acoustic interferences. The nature of these adjustments, and, in general, the considerations which determine the mouth area of a given horn are known to those skilled in the art.

The profiles of several members of the family of horns and a comparison of the flare of the horns with that of the exponential horn are shown in Fig. 2. The three horns here diagrammatically illustrated have identical throat and mouth areas. The exponential horn [4 falls between the horn I5 which approaches the conical shape and the horn Hi. It will be seen that horns following the equation given above for which the value of T is between zero and 1 have a smaller cross-sectional area at a given point on the axis than the exponential horn Hi. This characteristic is of importance in curved or reentrant horns, particularly in the higher frequency ranges, for the reason that the difference between the lengths of the extreme sound paths at the inside and the outside of the bent portions of the horn is less than, for example, that of the exponential horn. This means that interference effects at the bent portions of the sound passage are minimized. Advantage is taken of this particular feature of the invention in the horn illustrated in Fig. 5. In this double re-entrant horn, the sound generated by the driving motor I! is transmitted by means of the acoustic conduit I8, which may provide either a circular or an annular sound passageway, to the annular intermediate section l9 of the horn and thence through the outer annular section 20 to the atmosphere. The differences in the inside and outside acoustic paths indicated by the arrows 2| and 22 at the bent portions 23 and 24 of the acoustic passageway depend upon the cross-sectional areas of the acoustic passageway or horn at these points.

Although the curves of Fig. 3 represent the throat resistance characteristics of infinite horns, they may also .be taken to indicate a mean value or general trend of horns of finite length. These curves show that the rate of increase of throat resistance with increasing frequency immediately above the cut-off value increases with decreasing values of the parameter, T. These curves indicate that for the exponential horn (T=1) the throat resistant rises to the 10% tolerance zone on either side of ultimate throat resistance value at a frequency of 2.25 times the cut-off frequency. This point is reached at 1.3 times cut-off frequency when T is assigned a value of, 0.707, the throat resistance remaining below the, ultimate value throughout the entire frequency I range. Again, the desired throat resistance'range is reached at 1.1 times cut-off frequency when T is assigned a value of 0.6. In this case the resistance rises slightly above the ultimate value and gradually returns as the frequency-increases.

The two remaining curves of Fig. 3 show the throat resistance characteristics of other members of the horn family, indicating the wide range of characteristics obtainable which permits their adaptation to almost any type of driving'unit.

The efficiency of a horn having a given mouth area and cut-off frequency and defined by the equation given herein where T=0.6 is shown in Fig. 4. The efllciency-frequency relationship of a corresponding exponential horn is also given for comparison purposes. Both of these curves represent experimentally determined values.

As hereinbefore stated, the general principles which apply to the use of a horn in a sound radiating device, such as a radio loudspeaker, are also operative when the horn is used with a sound receiving device or as a transformer between acoustic channels having different crosssectional areas and therefore diiferent terminal impedances. Thus, the invention herein describedmay be employed with a microphone or as a part of a sound ranging device. By choosing the proper value for the parameter, a horn of this invention may be used to selectively emphasize predetermined frequencies. The specification of a horn to be used with a sound receiver may be entirely different from one which is considered to be suitable when used with a loudspeaker since in the former case uniformity of response at the expense of maximum conversion efllciency may be desired. Values of T between 0 and 0.5 will provide selective pick-up of frequencies near cut-oif with the usual acousto-electric generator; values of T near 0.6'produce a more uniform response over a wider band.

When used as a coupling transformer between two sections of an acoustic system, it is generally desirable that reflections from the coupling element be minimized in order that transmission through the line may be accomplished as efficiently as possible. Such an element is provided in a horn whose parameter, T, is approximately An outstanding advantage of the invention as it relates to the family as a whole is the great flexibility of the acoustic characteristics of the horns. The multitude of different conditions which occur with different types of equipment and for different applications may be met by means of the invention. I

S=S, cosh g d-T sinh where S=cross-sectional area at distance x from the throat of the horn measured along the mean acoustic path thereof 27rfo c being the velocity of sound and fo the cutoff frequency of the horn T is a constant having a positive finite value other than unity.

2. An acoustic horn whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance with the law a: z 2 S=S,(cosh T smh where S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof m 0 being the velocity of sound and fo the cut off frequency of the horn T is a. constant having a positive value of less than unity.

3. An acoustic horn whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance with the law a: a: 3 S-S,(cosh T 8111b where S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof L t c being the velocity of sound and fo the cutoff frequency of the horn T is a constant having a finite value greater than unity.

4. An acoustic horn whose cross-section area increases from a value St at the throat of the horn substantially in accordance with the law 2 S=S,(cosh 2+7 sinh i) where S=cr0ss-sectiona1 area at distance a: from the throat of the horn measured along the mean acoustic path thereof 0 being the velocity of sound and fo the cutoff frequency of the horn T is a constant having a value of approximately 5. An acoustic horn whose cross-sectional area increases from a value St at the throat of the horn substantially inaccordance with the law 2 S: S (cosh S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof where 0 being the velocity of sound and fo the cutoff frequency of the horn 6. An acoustic horn whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance with the law I S=S,(cosh 2+7 Binh g where S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof 0 being the velocity of sound and fo the cutoff frequency of the horn the value of T being such that predetermined horn throat resistance characteristics are obtained.

7. An acoustic horn whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance with the law 2 S= S, cosh T sinh where S=cross-sectional area at distance x from the throat of the horn measured along the mean acoustic path thereof .i *fo 0 being the velocity of sound and fo the cuton frequency of the horn the value of T being that which results in a horn throat resistance which deviates less than ten per cent from ultimate value over a maximum frequency range.

8. An acoustic horn whose cross-sectional area increases from a value S: at the throat of the horn substantially in accordance with the law 2 S=iS,(cosh 3 T sinh where S=cross'-sectional area at distance' a: from the throat of'the horn measured along the mean acoustic path thereof being the velocity of sound and fo the cutoff frequency of the horn -T is a constant having a positive value of less than unity,

the acoustic resistance of said horn deviating less than ten per cent from ultimate value at all audible frequencies greater than twice cut-off frequency.

9. An acoustic horn in accordance with claim 1 and having a mouth whose area is greater than that of an equivalent circular horn mouth having a circumference equal to the length of the sound wave at cut-off frequency.

10. An acoustic horn in accordance with claim 1 and having a mouth whose area is greater than that of an equivalent circular horn mouth having a circumference equal to one-half the length of the sound wave at cut-off frequency.

11. In an electroacoustic sound reproducing device including an electrical signal source and electromechanical driving unit having an established mechanical impedance, an acoustic conduit whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance with the law a: a: 2 S=S,(cosh d-T 511111 where S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof 0 being the velocity of sound and fo the cutoff frequency of the horn,

the values of St and of the parameter T being such that the throat impedance of said horn is substantially the conjugate of the mechanical impedance of said electrical signal source and driving unit over the frequency range from 1.5 to 5 times cut-off frequency.

12. In an electroacoustic sound reproducing device including an electrical Signal source and an electromechanical driving unit having established mechanical reactance characteristics an acoustic horn coupled to said driving unit and comprising an acoustic conduit whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance .with the law i i 2 SS,(cosh T SlIlh where S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof 0 being the velocity of sound and fo the cutoff frequency of the horn,

a a 2 S S (cosh -i- T smh where S=cross-sectiona1 area at distance a: from the throat of the horn measured along the mean acoustic path thereof i "fo c being the velocity of sound and ft the cutoff frequency of the horn T is a constant having a positive value less than 14. In an acoustic system including acoustic conduits of different cross-sectional areas, an acoustic connector comprising a conduit whose terminal cross-sectional areas are equal to the cross-sectional areas of the respective acoustic conduits connected thereby, the cross-sectional area of said connector increasing from a value St at the small end thereof substantially in accordance with the law S=cross-sectional area at distance :0 from the small end of the connector measured along the mean acoustic path thereof L *21 f0 0 being the velocity of sound and fo the cutoif frequency of the connector T is a constant having a value of approximately 15.. An acoustic horn of the re-entrant type comprising a retroverted acoustic conduit whose cross-sectional area increases from a value St at the throat of the horn substantially in accordance with the law 2 S=S,(cosh %+T sinh g where S=cross-sectional area at distance a: from the throat of the horn measured along the mean acoustic path thereof 0 being the velocity of sound and ,fo the cutoff frequency of the horn T is a constant having a positive value between zero and unity.

16. The acoustic horn of claim 13 when. the

acoustic passageway within said conduit at a bent portion thereof is annular in cross-section.

17. An acoustic horn of the re-entrant type comprising a retroverted acoustic conduit whose cross-sectional area increases from a "alue S:

at the throat 01' the horn substantially in accordance with the law z I s=s.(cosh where B=cross-sectional area at distance a: from the throat of the horn measured along vthe mean acoustic path thereof VINCENT SALMON. 

